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Answer :
Final answer:
The derivative of the function y=3x(3x²−5x) is found using the product rule of differentiation and is equal to 9x³+3x²-15x. None of the given options matches this result.
Explanation:
To find the derivative of the function y=3x(3x²−5x), we can make use of the product and power rules of differentiation.
Firstly we need to differentiate the function which is a product of 3x and (3x²−5x). According to the product rule, the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.
So, if we let u=3x and v=(3x²−5x), then y'=u'v + uv'.
By calculating the derivatives, we find that u'=3, v'=2x(3) -5 = 6x -5.
Substituting these back into our formula for y' gives us y'=3*(6x-5) + (3x)*(3x²−5x)=18x²−15x + 9x³−15x²=9x³+3x²-15x.
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